Energy can't be created or destroyed — only transformed, and now integrated. From a stretched spring to a satellite in orbit, it's all one bookkeeping system.
Episode Guide — Season 3
K = ½mv² looks simple until you realize it's frame-dependent — two observers moving relative to each other measure two different kinetic energies for the same object.
Work is a line integral — F·dr summed along a path. Conservative forces don't care which path you take; friction always does.
Potential energy is what you get when you integrate a conservative force backward. Springs, gravity near a surface, and gravity far from it all follow the same pattern — just different functions.
Pick your system carefully and total energy never changes — it just trades forms. Energy bar charts make the bookkeeping visual before the algebra starts.
Power is just work's rate of change — how fast energy moves. The instantaneous version, P = F·v, connects straight back to Unit 2's forces.